{
 "cells": [
  {
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   "cell_type": "markdown",
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   "source": [
    "# Plot Conditional Adjusted Predictions\n",
    "\n",
    "This notebook shows how to use, and the capabilities, of the `plot_predictions` function. The `plot_predictions` function is a part of Bambi's sub-package `interpret` that features a set of tools used to interpret complex regression models that is inspired by the R package [marginaleffects](https://marginaleffects.com/chapters/predictions.html#conditional-predictions). "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting Generalized Linear Models\n",
    "\n",
    "The purpose of the _generalized linear model_ (GLM) is to unify the approaches needed to analyze data for which either: (1) the assumption of a linear relation between $x$ and $y$, or (2) the assumption of normal variation is not appropriate. GLMs are typically specified in three stages:\n",
    "\n",
    "1. the linear predictor $\\eta = X\\beta$ where $X$ is an $n$ x $p$ matrix of explanatory variables.\n",
    "2. the link function $g(\\cdot)$ that relates the linear predictor to the mean of the outcome variable $\\mu = g^{-1}(\\eta) = g^{-1}(X\\beta)$\n",
    "3. the random component specifying the distribution of the outcome variable $y$ with mean $\\mathbb{E}(y|X) = \\mu$.\n",
    "\n",
    "Based on these three specifications, the mean of the distribution of $y$, given $X$, is determined by $X\\beta: \\mathbb{E}(y|X) = g^{-1}(X\\beta)$. \n",
    "\n",
    "GLMs are a broad family of models where the output $y$ is typically assumed to follow an exponential family distribution, e.g., Binomial, Poisson, Gamma, Exponential, and Normal. The job of the link function is to map the linear space of the model $X\\beta$ onto the non-linear space of a parameter like $\\mu$. Commonly used link function are the _logit_ and _log_ link. Also known as the _canonical_ link functions. This brief introduction to GLMs is not meant to be exhuastive, and another good starting point is the Bambi [Basic Building Blocks](https://bambinos.github.io/bambi/notebooks/how_bambi_works.html#Link-functions) example.\n",
    "\n",
    "Due to the link function, there are typically three quantities of interest to interpret in a GLM:\n",
    "\n",
    "1. the linear predictor $\\eta$\n",
    "2. the mean $\\mu = g^{-1}(\\eta)$\n",
    "3. the response variable $Y \\sim \\mathcal{D}(\\mu, \\theta)$ where $\\mu$ is the mean parameter and $\\theta$ is (possibly) a vector that contains all the other \"nuisance\" parameters of the distribution.\n",
    "\n",
    "As modelers, we are usually more interested in interpreting (2) and (3). However, $\\mu$ is not always on the same scale of the response variable and can be more difficult to interpret. Rather, the response scale is a more interpretable scale. Additionally, it is often the case that modelers would like to analyze how a model parameter varies across a range of explanatory variable values. To achieve such an analysis, Bambi has taken inspiration from the R package marginaleffects, and implemented a `plot_predictions` function that plots the conditional adjusted predictions to aid in the interpretation of GLMs. Below, it is briefly discussed what are conditionally adjusted predictions, how they are computed, and ultimately how to use the `plot_predictions` function."
   ]
  },
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   "metadata": {},
   "source": [
    "## Conditionally Adjusted Predictions\n",
    "\n",
    "Adjusted predictions refers to the outcome predicted by a fitted model on a specified scale for a given combination of values of the predictor variables, such as their observed values, their means, or some user specified grid of values. The specification of the scale to make the predictions, the link or response scale, refers to the scale used to estimate the model. In normal linear regression, the link scale and the response scale are identical, and therefore, the adjusted prediction is expressed as the mean value of the response variable at the given values of the predictor variables. On the other hand, a logistic regression's link and response scale are not identical. An adjusted prediction on the link scale will be represented as the log-odds of a successful response given values of the predictor variables. Whereas an adjusted prediction on the response scale gives the probability that the response variable equals 1. The conditional part of conditionally adjusted predictions represents the specific predictor(s) and its values we would like to condition on when plotting predictions."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing Adjusted Predictions\n",
    "\n",
    "The objective of plotting conditional adjusted predictions is to visualize how a parameter of the (conditional) response distribution varies as a function of (some) explanatory variables. In `predictions`, there are three scenarios to compute conditional adjusted predictions:\n",
    "\n",
    "1. user provided values \n",
    "2. a grid of equally spaced and central values\n",
    "3. empirical distribution (original data used to fit the model)\n",
    "\n",
    "In the case of (1) above, a dictionary is passed with the explanatory variables as keys, and the values to condition on are the values. With this dictionary, Bambi assembles all pairwise combinations (transitions) of the specified explanatory variables into a new \"hypothetical\" dataset. Covariates not existient in the dictionary are held at their mean or mode. \n",
    "\n",
    "In (2), a string or list is passed with the name(s) of the explanatory variable(s) to create a grid of equally spaced values. This is done by holding all other explanatory variables constant at some specified value, a _reference grid_, that may or may not correspond to actual observations in the dataset used to fit the model. By default, the `plot_predictions` function uses a grid of 200 equally spaced values between the minimum and maximum values of the specified explanatory variable as the reference grid.\n",
    "\n",
    "Lastly, in (3), the original data used to fit the model is used to compute predictions. This is known as _unit level_ predictions.\n",
    "\n",
    "Using the data, from scenario 1, 2, or 3, the `plot_predictions` function uses the fitted model to then compute the predictions. The `plot_predictions` function then uses these predictions to plot the model parameter as a function of (some) explanatory variable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import warnings\n",
    "\n",
    "import bambi as bmb\n",
    "\n",
    "warnings.simplefilter(action=\"ignore\", category=FutureWarning)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Linear Model\n",
    "\n",
    "For the first demonstration, we will use a Gaussian linear regression model with the `mtcars` dataset to better understand the `plot_predictions` function and its arguments. The `mtcars` dataset was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973--74 models). The following is a brief description of the variables in the dataset:\n",
    "\n",
    "- mpg: Miles/(US) gallon\n",
    "- cyl: Number of cylinders\n",
    "- disp: Displacement (cu.in.)\n",
    "- hp: Gross horsepower\n",
    "- drat: Rear axle ratio\n",
    "- wt: Weight (1000 lbs)\n",
    "- qsec: 1/4 mile time\n",
    "- vs: Engine (0 = V-shaped, 1 = straight)\n",
    "- am: Transmission (0 = automatic, 1 = manual)\n",
    "- gear: Number of forward gear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sigma, hp, wt, hp:wt, cyl, gear]\n"
     ]
    },
    {
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 13 seconds.\n"
     ]
    }
   ],
   "source": [
    "# Load data\n",
    "data = bmb.load_data('mtcars')\n",
    "data[\"cyl\"] = data[\"cyl\"].replace({4: \"low\", 6: \"medium\", 8: \"high\"})\n",
    "data[\"gear\"] = data[\"gear\"].replace({3: \"A\", 4: \"B\", 5: \"C\"})\n",
    "data[\"cyl\"] = pd.Categorical(data[\"cyl\"], categories=[\"low\", \"medium\", \"high\"], ordered=True)\n",
    "\n",
    "# Define and fit the Bambi model\n",
    "model = bmb.Model(\"mpg ~ 0 + hp * wt + cyl + gear\", data)\n",
    "idata = model.fit(draws=1000, target_accept=0.95, random_seed=1234)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can print the Bambi model object to obtain the model components. Below, we see that the Gaussian linear model uses an identity link function that results in no transformation of the linear predictor to the mean of the outcome variable, and the distrbution of the likelihood is Gaussian."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Default values\n",
    "\n",
    "Now that we have fitted the model, we can visualize how a model parameter varies as a function of (some) interpolated covariate. For this example, we will visualize how the mean response `mpg` varies as a function of the covariate `hp`. \n",
    "\n",
    "The Bambi model, ArviZ inference data object (containing the posterior samples and the data used to fit the model), and a list or dictionary of covariates, in this example only `hp`, are passed to the `plot_predictions` function. The `plot_predictions` function then computes the conditional adjusted predictions for each `covariate` in the list or dictionary using the method described above. The `plot_predictions` function returns a `matplotlib` figure object that can be further customized.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Default computed for conditional variable: hp\n",
      "Default computed for unspecified variable: cyl, gear, wt\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"hp\", ax=ax);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we talk about the plot, you will notice that some messages have been logged to the console. By default `interpret` is _verbose_ and logs a message to the console if a default value is computed for covariates in `conditional`. This is useful because unless the documentation is read, it can be difficult to tell which covariates are having default values computed for. Thus, Bambi has a config file `bmb.config[\"INTERPRET_VERBOSE\"]` where we can specify whether or not to log messages. By default, this is set to true. To turn off logging, set `bmb.config[\"INTERPRET_VERBOSE\"] = False`. From here on, we will turn off logging.\n",
    "\n",
    "The plot above shows that as `hp` increases, the mean `mpg` decreases. As stated above, this insight was obtained by creating the reference grid and then using the fitted model to compute the predicted values of the model parameter, in this example `mpg`, at each value of the reference grid.\n",
    "\n",
    "By default, `plot_predictions` uses the highest density interval (HDI) of the posterior distribution to compute the credible interval of the conditional adjusted predictions. The HDI is a Bayesian analog to the frequentist confidence interval. The HDI is the shortest interval that contains a specified probability of the posterior distribution. By default, `plot_predictions` uses the 94% HDI.\n",
    "\n",
    "`plot_predictions` uses the posterior distribution by default to visualize some mean outcome parameter . However, the posterior predictive distribution can also be plotted by specifying `pps=True` where `pps` stands for posterior predictive samples of the response variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmb.config[\"INTERPRET_VERBOSE\"] = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"hp\", pps=True, ax=ax);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we notice that the uncertainty in the conditional adjusted predictions is much larger than the uncertainty when `pps=False`. This is because the posterior predictive distribution accounts for the uncertainty in the model parameters and the uncertainty in the data. Whereas, the posterior distribution only accounts for the uncertainty in the model parameters.\n",
    "\n",
    "Additionally, `predictions` can be called to obtain a summary dataframe of the data, mean predictions (estimate), and uncertainty interval. The covariate columns in this dataframe is used to create the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hp</th>\n",
       "      <th>cyl</th>\n",
       "      <th>gear</th>\n",
       "      <th>wt</th>\n",
       "      <th>estimate</th>\n",
       "      <th>lower_3.0%</th>\n",
       "      <th>upper_97.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>52</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>21.810412</td>\n",
       "      <td>15.363036</td>\n",
       "      <td>27.695004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>57</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>21.728002</td>\n",
       "      <td>14.799208</td>\n",
       "      <td>27.695061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>63</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>21.470226</td>\n",
       "      <td>15.192043</td>\n",
       "      <td>27.603438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>69</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>21.251466</td>\n",
       "      <td>14.876009</td>\n",
       "      <td>26.865749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>75</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>21.117730</td>\n",
       "      <td>15.416268</td>\n",
       "      <td>27.389751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>80</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>20.818311</td>\n",
       "      <td>15.323215</td>\n",
       "      <td>26.810713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>86</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>20.619549</td>\n",
       "      <td>14.916622</td>\n",
       "      <td>26.441445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>20.464403</td>\n",
       "      <td>14.924356</td>\n",
       "      <td>26.002963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>98</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>20.229962</td>\n",
       "      <td>15.119724</td>\n",
       "      <td>25.877523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>103</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>3.21725</td>\n",
       "      <td>20.093819</td>\n",
       "      <td>14.936911</td>\n",
       "      <td>25.902589</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    hp   cyl gear       wt   estimate  lower_3.0%  upper_97.0%\n",
       "0   52  high    A  3.21725  21.810412   15.363036    27.695004\n",
       "1   57  high    A  3.21725  21.728002   14.799208    27.695061\n",
       "2   63  high    A  3.21725  21.470226   15.192043    27.603438\n",
       "3   69  high    A  3.21725  21.251466   14.876009    26.865749\n",
       "4   75  high    A  3.21725  21.117730   15.416268    27.389751\n",
       "5   80  high    A  3.21725  20.818311   15.323215    26.810713\n",
       "6   86  high    A  3.21725  20.619549   14.916622    26.441445\n",
       "7   92  high    A  3.21725  20.464403   14.924356    26.002963\n",
       "8   98  high    A  3.21725  20.229962   15.119724    25.877523\n",
       "9  103  high    A  3.21725  20.093819   14.936911    25.902589"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_df = bmb.interpret.predictions(model, idata, \"hp\", pps=True)\n",
    "summary_df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`plot_predictions` allows up to three covariates to be plotted simultaneously where the first element in the list represents the main (x-axis) covariate, the second element the group (hue / color), and the third element the facet (panel). However, when plotting more than one covariate, it can be useful to pass specific `group` and `panel` arguments to aid in the interpretation of the plot. Therefore, `subplot_kwargs` allows the user to manipulate the plotting by passing a dictionary where the keys are `{\"main\": ..., \"group\": ..., \"panel\": ...}` and the values are the names of the covariates to be plotted. For example, passing two covariates `hp` and `wt` and specifying `subplot_kwargs={\"main\": \"hp\", \"group\": \"wt\", \"panel\": \"wt\"}`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bmb.interpret.plot_predictions(\n",
    "    model=model, \n",
    "    idata=idata, \n",
    "    conditional={\"hp\": np.linspace(50, 350, 50), \"wt\": np.linspace(1, 6, 5)},\n",
    "    legend=False,\n",
    "    subplot_kwargs={\"main\": \"hp\", \"group\": \"wt\", \"panel\": \"wt\"},\n",
    "    fig_kwargs={\"figsize\": (20, 8), \"sharey\": True}\n",
    ")\n",
    "plt.tight_layout();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore, categorical covariates can also be plotted. We plot the the mean `mpg` as a function of the two categorical covariates `gear` and `cyl` below. The `plot_predictions` function automatically plots the conditional adjusted predictions for each level of the categorical covariate. Furthermore, when passing a list of covariates into the `plot_predictions` function, the list will be converted into a dictionary object where the key is taken from (\"horizontal\", \"color\", \"panel\") and the values are the names of the variables. By default, the first element of the list is specified as the \"horizontal\" covariate, the second element of the list is specified as the \"color\" covariate, and the third element of the list is mapped to different plot panels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, [\"gear\", \"cyl\"], ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User provided values\n",
    "\n",
    "In the previous example, default values were computed to construct a reference grid to compute the conditional adjusted predictions. We can also pass our own values for the covariates into `conditional` using a dictionary where the key-value pairs are the covariate and value(s) of interest. For example, if we wanted to compute the predictions for `hp=100`,  `wt=[1.5, 3.5]`, and `cyl=[\"low\", \"medium\", \"high\"]` we would pass the following dictionary in the code block below. As can be seen, several data types can be passed such as: `np.ndarray`, `list`, `int`, `float`, and `str`. \n",
    "\n",
    "Furthermore, Bambi by default, maps the order of the dict keys to the main, group, and panel of the matplotlib figure. Below, since `hp` is the first key, this is used for the x-axis, `wt` for the group (color), and `cyl` for the panel (facet)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bmb.interpret.plot_predictions(\n",
    "    model,\n",
    "    idata,\n",
    "    conditional={\n",
    "        \"hp\": [100, 120],\n",
    "        \"wt\": np.array([1.5, 3.5]),\n",
    "        \"cyl\": [\"low\", \"medium\", \"high\"]\n",
    "        },\n",
    "   fig_kwargs={\"figsize\": (10, 4), \"sharey\": True}\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before the plot is described, lets see how the dictionary passed to `conditional` was used to create the dataset in order to compute predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hp</th>\n",
       "      <th>wt</th>\n",
       "      <th>cyl</th>\n",
       "      <th>gear</th>\n",
       "      <th>estimate</th>\n",
       "      <th>lower_3.0%</th>\n",
       "      <th>upper_97.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100</td>\n",
       "      <td>1.5</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>26.610587</td>\n",
       "      <td>22.075256</td>\n",
       "      <td>31.146191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100</td>\n",
       "      <td>1.5</td>\n",
       "      <td>low</td>\n",
       "      <td>A</td>\n",
       "      <td>27.251230</td>\n",
       "      <td>23.419253</td>\n",
       "      <td>30.830434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>1.5</td>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>25.529368</td>\n",
       "      <td>20.970476</td>\n",
       "      <td>29.644434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100</td>\n",
       "      <td>3.5</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>19.101229</td>\n",
       "      <td>15.885756</td>\n",
       "      <td>22.376434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>3.5</td>\n",
       "      <td>low</td>\n",
       "      <td>A</td>\n",
       "      <td>19.741872</td>\n",
       "      <td>16.273313</td>\n",
       "      <td>23.045604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100</td>\n",
       "      <td>3.5</td>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>18.020010</td>\n",
       "      <td>15.563794</td>\n",
       "      <td>20.537324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>1.5</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>25.333773</td>\n",
       "      <td>21.137923</td>\n",
       "      <td>29.513798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>120</td>\n",
       "      <td>1.5</td>\n",
       "      <td>low</td>\n",
       "      <td>A</td>\n",
       "      <td>25.974416</td>\n",
       "      <td>21.920817</td>\n",
       "      <td>29.976438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>120</td>\n",
       "      <td>1.5</td>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>24.252554</td>\n",
       "      <td>19.666425</td>\n",
       "      <td>28.194181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>120</td>\n",
       "      <td>3.5</td>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>18.484655</td>\n",
       "      <td>15.674754</td>\n",
       "      <td>21.087136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>120</td>\n",
       "      <td>3.5</td>\n",
       "      <td>low</td>\n",
       "      <td>A</td>\n",
       "      <td>19.125298</td>\n",
       "      <td>15.718574</td>\n",
       "      <td>22.846968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>120</td>\n",
       "      <td>3.5</td>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>17.403436</td>\n",
       "      <td>15.073683</td>\n",
       "      <td>20.079422</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     hp   wt     cyl gear   estimate  lower_3.0%  upper_97.0%\n",
       "0   100  1.5    high    A  26.610587   22.075256    31.146191\n",
       "1   100  1.5     low    A  27.251230   23.419253    30.830434\n",
       "2   100  1.5  medium    A  25.529368   20.970476    29.644434\n",
       "3   100  3.5    high    A  19.101229   15.885756    22.376434\n",
       "4   100  3.5     low    A  19.741872   16.273313    23.045604\n",
       "5   100  3.5  medium    A  18.020010   15.563794    20.537324\n",
       "6   120  1.5    high    A  25.333773   21.137923    29.513798\n",
       "7   120  1.5     low    A  25.974416   21.920817    29.976438\n",
       "8   120  1.5  medium    A  24.252554   19.666425    28.194181\n",
       "9   120  3.5    high    A  18.484655   15.674754    21.087136\n",
       "10  120  3.5     low    A  19.125298   15.718574    22.846968\n",
       "11  120  3.5  medium    A  17.403436   15.073683    20.079422"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_df = bmb.interpret.predictions(\n",
    "    model,\n",
    "    idata,\n",
    "    conditional={\n",
    "        \"hp\": [100, 120],\n",
    "        \"wt\": np.array([1.5, 3.5]),\n",
    "        \"cyl\": [\"low\", \"medium\", \"high\"]\n",
    "        },\n",
    ")\n",
    "summary_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When a dictionary is passed, that informs Bambi that the user wants to compute predictions on user provided values. Thus, a pairwise grid is constructed using the dictionary values. Otherwise, a dataframe of unequal array lengths cannot be constructed. Furthermore, since `gear` was not passed as a key, but was a term in the model, the default value of `A` was computed for it.\n",
    "\n",
    "Given we now know that a pairwise grid was computed usiong the `conditional` dict, One interpretation of the plot above is that across all cylinder groups, a larger `wt` results in a lower mean `mpg`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unit level predictions\n",
    "\n",
    "In the previous example, user provided values were computed to construct a pairwise grid to compute the conditional adjusted predictions. It is also possible to compute predictions using the observed (empirical) data used to fit the model and then average over a specific or set of covariates to obtain average adjusted predictions. This is known as unit level predictions. To compute unit level predictions, do not pass any values to the `conditional` arg. and or specify `None` (the default)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cyl</th>\n",
       "      <th>gear</th>\n",
       "      <th>hp</th>\n",
       "      <th>wt</th>\n",
       "      <th>estimate</th>\n",
       "      <th>lower_3.0%</th>\n",
       "      <th>upper_97.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>medium</td>\n",
       "      <td>B</td>\n",
       "      <td>110</td>\n",
       "      <td>2.620</td>\n",
       "      <td>22.264986</td>\n",
       "      <td>20.077966</td>\n",
       "      <td>24.325617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>medium</td>\n",
       "      <td>B</td>\n",
       "      <td>110</td>\n",
       "      <td>2.875</td>\n",
       "      <td>21.349633</td>\n",
       "      <td>19.300573</td>\n",
       "      <td>23.263729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>low</td>\n",
       "      <td>B</td>\n",
       "      <td>93</td>\n",
       "      <td>2.320</td>\n",
       "      <td>25.918932</td>\n",
       "      <td>24.225028</td>\n",
       "      <td>27.517733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>110</td>\n",
       "      <td>3.215</td>\n",
       "      <td>18.734764</td>\n",
       "      <td>16.213729</td>\n",
       "      <td>21.265602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>175</td>\n",
       "      <td>3.440</td>\n",
       "      <td>16.940081</td>\n",
       "      <td>15.228838</td>\n",
       "      <td>18.599391</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      cyl gear   hp     wt   estimate  lower_3.0%  upper_97.0%\n",
       "0  medium    B  110  2.620  22.264986   20.077966    24.325617\n",
       "1  medium    B  110  2.875  21.349633   19.300573    23.263729\n",
       "2     low    B   93  2.320  25.918932   24.225028    27.517733\n",
       "3  medium    A  110  3.215  18.734764   16.213729    21.265602\n",
       "4    high    A  175  3.440  16.940081   15.228838    18.599391"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_df = bmb.interpret.predictions(\n",
    "    model,\n",
    "    idata,\n",
    "    conditional=None\n",
    ")\n",
    "summary_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cyl</th>\n",
       "      <th>gear</th>\n",
       "      <th>hp</th>\n",
       "      <th>wt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>medium</td>\n",
       "      <td>B</td>\n",
       "      <td>110</td>\n",
       "      <td>2.620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>medium</td>\n",
       "      <td>B</td>\n",
       "      <td>110</td>\n",
       "      <td>2.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>low</td>\n",
       "      <td>B</td>\n",
       "      <td>93</td>\n",
       "      <td>2.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>medium</td>\n",
       "      <td>A</td>\n",
       "      <td>110</td>\n",
       "      <td>3.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>high</td>\n",
       "      <td>A</td>\n",
       "      <td>175</td>\n",
       "      <td>3.440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      cyl gear   hp     wt\n",
       "0  medium    B  110  2.620\n",
       "1  medium    B  110  2.875\n",
       "2     low    B   93  2.320\n",
       "3  medium    A  110  3.215\n",
       "4    high    A  175  3.440"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# data used to fit the model\n",
    "model.data[[\"cyl\", \"gear\", \"hp\", \"wt\"]].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the data in the summary dataframe and model data are the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Marginalizing over covariates\n",
    "\n",
    "Since the empirical distrubution is used for computing predictions, the same number of rows ($32$) is returned as the data used to fit the model. To average over a covariate, use the `average_by` argument. If `True` is passed, then `predictions` averages over all covariates and a single estimate is returned. Else, if a single or list of covariates are passed, then `predictions` averages by the covariates passed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>estimate</th>\n",
       "      <th>lower_3.0%</th>\n",
       "      <th>upper_97.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20.076678</td>\n",
       "      <td>17.900002</td>\n",
       "      <td>22.221902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    estimate  lower_3.0%  upper_97.0%\n",
       "0  20.076678   17.900002    22.221902"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_df = bmb.interpret.predictions(\n",
    "    model,\n",
    "    idata,\n",
    "    conditional=None,\n",
    "    average_by=True\n",
    ")\n",
    "summary_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Average by subgroups\n",
    "\n",
    "It is still possible to plot predictions when computing unit level predictions. However, now a covariate(s) must be passed to `average_by` to obtain average adjusted predictions by group. In the plot below, we obtain average predictions grouped by `gear` and `cyl`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bmb.interpret.plot_predictions(\n",
    "    model,\n",
    "    idata,\n",
    "    conditional=None,\n",
    "    average_by=[\"gear\", \"cyl\"],\n",
    "    fig_kwargs={\"figsize\": (7, 3)},\n",
    ");"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Binomial Model\n",
    "\n",
    "Lets move onto a model that uses a distribution that is a member of the exponential distribution family and utilizes a link function. For this, we will implement the Negative binomial model from the students absences [example](https://bambinos.github.io/bambi/notebooks/negative_binomial.html#Negative-binomial-in-GLM). School administrators study the attendance behavior of high school juniors at two schools. Predictors of the number of days of absence include the type of program in which the student is enrolled and a standardized test in math. We have attendance data on 314 high school juniors. The variables of insterest in the dataset are the following:\n",
    "\n",
    "- daysabs: The number of days of absence. It is our response variable.\n",
    "- progr: The type of program. Can be one of ‘General’, ‘Academic’, or ‘Vocational’.\n",
    "- math: Score in a standardized math test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [alpha, prog, scale(math), prog:scale(math)]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8a41306b0994443a8a8b27c70c5545c3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "# Load data, define and fit Bambi model\n",
    "data = pd.read_stata(\"https://stats.idre.ucla.edu/stat/stata/dae/nb_data.dta\")\n",
    "data[\"prog\"] = data[\"prog\"].map({1: \"General\", 2: \"Academic\", 3: \"Vocational\"})\n",
    "\n",
    "model_interaction = bmb.Model(\n",
    "    \"daysabs ~ 0 + prog + scale(math) + prog:scale(math)\",\n",
    "    data,\n",
    "    family=\"negativebinomial\"\n",
    ")\n",
    "idata_interaction = model_interaction.fit(\n",
    "    draws=1000, target_accept=0.95, random_seed=1234, chains=4\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model utilizes a log link function and a negative binomial distribution for the likelihood. Also note that this model also contains an interaction `prog:sale(math)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: daysabs ~ 0 + prog + scale(math) + prog:scale(math)\n",
       "        Family: negativebinomial\n",
       "          Link: mu = log\n",
       "  Observations: 314\n",
       "        Priors: \n",
       "    target = mu\n",
       "        Common-level effects\n",
       "            prog ~ Normal(mu: [0. 0. 0.], sigma: [5.0102 7.4983 5.2746])\n",
       "            scale(math) ~ Normal(mu: 0.0, sigma: 2.5)\n",
       "            prog:scale(math) ~ Normal(mu: [0. 0.], sigma: [6.1735 4.847 ])\n",
       "        \n",
       "        Auxiliary parameters\n",
       "            alpha ~ HalfCauchy(beta: 1.0)\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_interaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(\n",
    "    model_interaction, \n",
    "    idata_interaction, \n",
    "    \"math\", \n",
    "    ax=ax, \n",
    "    pps=False\n",
    ");"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above shows that as `math` increases, the mean `daysabs` decreases. However, as the model contains an interaction term, the effect of `math` on `daysabs` depends on the value of `prog`. Therefore, we will use `plot_predictions` to plot the conditional adjusted predictions for each level of `prog`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(\n",
    "    model_interaction, \n",
    "    idata_interaction, \n",
    "    [\"math\", \"prog\"], \n",
    "    ax=ax, \n",
    "    pps=False\n",
    ");"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Passing specific `subplot_kwargs` can allow for a more interpretable plot. Especially when the posterior predictive distribution plot results in overlapping credible intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bmb.interpret.plot_predictions(\n",
    "    model_interaction, \n",
    "    idata_interaction, \n",
    "    conditional=[\"math\", \"prog\"],\n",
    "    pps=True,\n",
    "    subplot_kwargs={\"main\": \"math\", \"group\": \"prog\", \"panel\": \"prog\"},\n",
    "    legend=False,\n",
    "    fig_kwargs={\"figsize\": (16, 5), \"sharey\": True}\n",
    ");"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "\n",
    "To further demonstrate the `plot_predictions` function, we will implement a logistic regression model. This example is taken from the marginaleffects `plot_predictions` [documentation](https://marginaleffects.com/chapters/predictions.html#conditional-predictions). The internet movie database, http://imdb.com/, is a website devoted to collecting movie data supplied by studios and fans. It claims to be the biggest movie database on the web and is run by Amazon. The movies in this dataset were selected for inclusion if they had a known length and had been rated by at least one imdb user. The dataset below contains 28,819 rows and 24 columns. The variables of interest in the dataset are the following:\n",
    "- title. Title of the movie.\n",
    "- year. Year of release.\n",
    "- budget. Total budget (if known) in US dollars\n",
    "- length. Length in minutes.\n",
    "- rating. Average IMDB user rating.\n",
    "- votes. Number of IMDB users who rated this movie.\n",
    "- r1-10. Multiplying by ten gives percentile (to nearest 10%) of users who rated this movie a 1.\n",
    "- mpaa. MPAA rating.\n",
    "- action, animation, comedy, drama, documentary, romance, short. Binary variables represent- ing if movie was classified as belonging to that genre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Modeling the probability that certified_fresh==1\n",
      "Initializing NUTS using adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [length, style, length:style]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7073ab77d0e3404baad500272661ef2d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 374 seconds.\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/ggplot2movies/movies.csv\")\n",
    "\n",
    "data[\"style\"] = \"Other\"\n",
    "data.loc[data[\"Action\"] == 1, \"style\"] = \"Action\"\n",
    "data.loc[data[\"Comedy\"] == 1, \"style\"] = \"Comedy\"\n",
    "data.loc[data[\"Drama\"] == 1, \"style\"] = \"Drama\"\n",
    "data[\"certified_fresh\"] = (data[\"rating\"] >= 8) * 1\n",
    "data = data[data[\"length\"] < 240]\n",
    "\n",
    "priors = {\"style\": bmb.Prior(\"Normal\", mu=0, sigma=2)}\n",
    "model = bmb.Model(\"certified_fresh ~ 0 + length * style\", data=data, priors=priors, family=\"bernoulli\")\n",
    "idata = model.fit(random_seed=1234, target_accept=0.9, init=\"adapt_diag\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic regression model uses a logit link function and a Bernoulli likelihood. Therefore, the link scale is the log-odds of a successful response and the response scale is the probability of a successful response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: certified_fresh ~ 0 + length * style\n",
       "        Family: bernoulli\n",
       "          Link: p = logit\n",
       "  Observations: 58662\n",
       "        Priors: \n",
       "    target = p\n",
       "        Common-level effects\n",
       "            length ~ Normal(mu: 0.0, sigma: 0.0283)\n",
       "            style ~ Normal(mu: 0.0, sigma: 2.0)\n",
       "            length:style ~ Normal(mu: [0. 0. 0.], sigma: [0.0263 0.0263 0.0263])\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, by default, the `plot_predictions` function plots the mean outcome on the response scale. Therefore, the plot below shows the probability of a successful response `certified_fresh` as a function of `length`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"length\", ax=ax);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, we can see how the probability of `certified_fresh` varies as a function of categorical covariates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"style\", ax=ax);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting other model parameters\n",
    "\n",
    "`plot_predictions` also has the argument `target` where `target` determines what parameter of the response distribution is plotted as a function of the explanatory variables. This argument is useful in distributional models, i.e., when the response distribution contains a parameter for location, scale and or shape. The default of this argument is `mean` and passing a parameter into `target` only works when the argument `pps=False` because when `pps=True` the posterior predictive distribution is plotted and thus, can only refer to the outcome variable (instead of any of the parameters of the response distribution). For this example, we will simulate our own dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [Intercept, x, alpha_Intercept, alpha_x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3792802aecbf4732b40231acfec7affa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 3 seconds.\n",
      "There were 9 divergences after tuning. Increase `target_accept` or reparameterize.\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng(121195)\n",
    "N = 200\n",
    "a, b = 0.5, 1.1\n",
    "x = rng.uniform(-1.5, 1.5, N)\n",
    "shape = np.exp(0.3 + x * 0.5 + rng.normal(scale=0.1, size=N))\n",
    "y = rng.gamma(shape, np.exp(a + b * x) / shape, N)\n",
    "data_gamma = pd.DataFrame({\"x\": x, \"y\": y})\n",
    "\n",
    "formula = bmb.Formula(\"y ~ x\", \"alpha ~ x\")\n",
    "model = bmb.Model(formula, data_gamma, family=\"gamma\")\n",
    "idata = model.fit(random_seed=1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: y ~ x\n",
       "                alpha ~ x\n",
       "        Family: gamma\n",
       "          Link: mu = inverse\n",
       "                alpha = log\n",
       "  Observations: 200\n",
       "        Priors: \n",
       "    target = mu\n",
       "        Common-level effects\n",
       "            Intercept ~ Normal(mu: 0.0, sigma: 2.5037)\n",
       "            x ~ Normal(mu: 0.0, sigma: 2.8025)\n",
       "    target = alpha\n",
       "        Common-level effects\n",
       "            alpha_Intercept ~ Normal(mu: 0.0, sigma: 1.0)\n",
       "            alpha_x ~ Normal(mu: 0.0, sigma: 1.0)\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model we defined uses a `gamma` distribution parameterized by `alpha` and `mu` where `alpha` utilizes a log link and `mu` goes through an inverse link. Therefore, we can plot either: (1) the `mu` of the response distribution (which is the default), or (2) `alpha` of the response distribution as a function of the explanatory variable $x$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First, the mean of the response (default)\n",
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"x\", ax=ax);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, instead of plotting the default target, `target=mean`, we set `target=alpha` to visualize how the model parameter `alpha` varies as a function of the `x` predictor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 840x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Second, another param. of the distribution: alpha\n",
    "fig, ax = plt.subplots(figsize=(7, 3), dpi=120)\n",
    "bmb.interpret.plot_predictions(model, idata, \"x\", target=\"alpha\", ax=ax);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Sep 28 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.7\n",
      "IPython version      : 9.4.0\n",
      "\n",
      "pandas    : 2.3.2\n",
      "numpy     : 2.3.3\n",
      "matplotlib: 3.10.6\n",
      "bambi     : 0.14.1.dev58+gb25742785.d20250928\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dev",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
